Critical Speedy Aw

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Critical Speed YawAnalysis and Testing

Presented by:

John Daily

Jackson Hole Scientific Investigations, Inc.Box 2206

Jackson, WY 83001


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Critical Speed Yaw

What is a yaw?

What does the word Critical mean?

How do we get Speed out of this?


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Definitions

Yaw refers to the orientation of the vehicle.

Specifically, the heading of the vehicle isnot co-linear with the velocity vector of the

vehicle. The evidence showing this are the tire

scuffs on the road.

The rear tires track outside the

corresponding front tires.


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Definitions, contd.

Critical refers to the idea that we may identifythe lateral acceleration as the maximumdynamic friction on the road.

We obtain this friction information with a test

skid. We may have to correct our test skid information

for grade or superelevation.

The ONLY way a vehicle gets onto a criticalspeed yaw is through the application of aninappropriate steering input (over correction)!


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Speed Calculation

To determine a speed

from a critical speed yaw

situation, we need the

radius of the curved path

of the vehicle center of

mass and the lateralacceleration of the

vehicle.

Lateral accelerationcomes from skid testing.

rfS 86.3=


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Radius Determination

In order to obtain a pathradius, we first measure a

chord of the arc left bythe outside front tire.

A chord is any line that

cuts the arc at two points. The chord beginning is

right after the rear tiremark crosses over the

front tire mark.

Chord lengths should bebetween 30 and 50 feet.


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Radius Determination, contd.

After we have laid downthe chord measurement,

we have to determine amiddle ordinate.

The middle ordinate

divides the chord in halfand extends out to far theedge of the tire mark.

For a 30 foot chord,

measure the middleordinate to the nearest1/8 inch.


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Radius Determination, contd.

Once we have chord and

middle ordinate

measurements, we may

calculate the radius of the

outside front tire mark

with the followingequation:

To get the CM radius,

subtract of the trackwidth from this

calculation.

28

2m

m

c

R +=


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Skid Testing

In order to get the proper drag factor for a

critical speed calculation, we must do testskids.

Results between tests must be consistent. The following tests were conducted at the

Wisconsin State Patrol Academy in August

2002.


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Vehicle Skid Tests

Two vehicles were used to develop drag factor data

A 2002 Pontiac Grand Prix was used to gather ABSbraking data

A 1997 Ford Crown Vic was used for both ABS and non-ABS testing

A VC-2000 accelerometer was used to gather the dragfactor data

The accelerometer data was graphed with data points

every 0.10 seconds The accelerometer was in the AutoStart mode, with a

default acceleration setting of -0.20g


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Vehicle Test Skids, contd

Investigators identified and measured the skid marksfrom the test vehicles

The whole length of the skid marks were difficult to pickup visually

An LTI Laser with a polarizer was used to assist indetermining visual skid length

These enhanced data correlated better with the skidlength as reported by the VC-2000

The rear brakes of the Ford did not lock up when the

ABS was disabled Hence, we were not able to get a true sliding drag factorfor this surface

The drag factor was for the Ford only


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Close-up of Sliding

Contact Patch


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Spackling indicates the tire is

braking at or near maximum.


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Skid Test Data

with Polarizer

n/a79.41088495.980n/aenhanced

178n/a907888.472n/ameasured

22297103849180n/adistance (VC)

4.342.943.012.522.622.442.43Max Time (VC)

0.7740.7460.7430.8310.8640.8670.858average G (VC)

1.0280.9580.9720.931.0171.081.03peak G (VC)

73.74849.14649.746.547.5Speed (VC)

724750464946n/aRadar

7654321Test Number


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Deceleration Factor Tests

for 1997 Ford Crown Victoria with ABS Disabled

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)

G

or

fw/o ABS(1)

w/o ABS(2)

1997 Crown Vic Tests

Rear Brakes did not lock up


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Deceleration Factor Tests

from VC2000 Accelerometer for 2002 Pontiac Grand Prix

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Time (sec)

G

or

f

Trial 1

Trial 2

Trial 3

All Pontiac ABS Tests


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Deceleration Factor Test

1997 Ford Crown Victoria with ABS Disabled

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time (sec)

G

's

Drag Factor

Average

Test skid from 73 mph


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Acceleration Factor Tests

from VC2000 Accelerometer

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sec)

Go

r

f

Trial 1

Trial 2

Trial 3

w / ABSw /o ABS(1)

w /o ABS(2)

hi speed

All Test Skids


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Road Evidence

In order to properly analyze a critical speed

yaw situation, we must recognize the tiremark evidence left behind.

Note the diagonal striations and unevenedge of the tire marks left in the following

photos.

The rear tires begin tracking outside thefront tires.


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Measuring Grade


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Measuring Super-elevation


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Yaw Marks (Scuffs)

Tire is sliding and rotating

A yaw results when the velocity

vector and heading of the vehicleare not co-linear.

If the yaw is the result of

inappropriate steering input, then

the yaw may be a Critical Speed

Yaw, and may be used for speed

analysis in a simple,

straightforward manner.

This photo illustrates a critical

speed yaw. Notice the rear tires

track outside the corresponding

front tires.


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Yaw Marks, Contd.

This crash began with

critical speed yaw marks

on the shoulder

We can use shoulder

drag to get a

conservative speedestimate.

We may average

shoulder and road drag toget an upper limit speed.


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Yaw Marks, Contd.

The Yaw begins to

transition to a side

skid. We may no

longer treat it as a

critical speed yaw. We will see later in

the presentation how

to deal with a spin-out.


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Yaw Marks, Contd.

Another example of

transitioning yaw

marks-

If these marks were

analyzed as criticalspeed yaws, the

speeds would be way

off probably on thehigh side


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Yaw Marks, Contd.

This is a curving tire

mark, but does not

indicate a yaw.

This is a curving

acceleration scuff.

Other curving marks mayalso look like critical

speed yaws, but are not.

Is there a way to examinethis question?


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Critical Speed Yaw?

We need a tool we can use to determine if the vehicle isactually in a critical speed yaw.

If we look at the dynamics of a vehicle in this maximumsteering situation, we would expect the vehicle todecelerate longitudinally as it progresses through theyaw.

If we can quantify this deceleration at a nominal value,then we may look at any particular case and determine ifits deceleration fits into the model.

Much testing over the years suggest a nominal value foryaw deceleration on a dry, hard-surfaced road, is about0.20g.


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Critical Speed Yaw? contd.

If we measure two chords and two middle

ordinates, we may calculate two radii. If the second chord is measured from theend of the first chord, we may calculate

the difference in radius between the firstchord and the second chord.

The second radius calculated should besmaller than the first if the vehicle isslowing.


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Critical Speed Yaw? contd.

Calculate a speed foreach radius.

Use the followingequation to determinethe deceleration in theyaw:

The distance d in theequation is from onemiddle ordinate to theother.

d

SSf

fo

30

22

=

Critical Speed Yaw Test


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Wisconsin Results The Ford was put into a critical speed yaw at 33

mph as measured by Radar

The VC-2000 was set in continuous mode tomeasure the longitudinal deceleration factor

The longitudinal deceleration was 0.18g to 0.23g A chord and middle ordinate was measuredwhen the rear tire began tracking outside the

corresponding front tire A second chord and middle ordinate was

measured from the end of the first chord


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Critical Speed Yaw Test, contd

A radius was calculated for each chord

If the vehicle is in a true critical speed yaw, there should

be a reduction in speed from the first radius to thesecond radius

We will calculate the speed using the standard critical

speed yaw equation and the drag factor from the Ford Because the rear wheels of the Ford did not lock up, this

speed calculation will be low

A second speed calculation, using the average ABS dragfactor for the Ford, results in a speed within one mph ofthe Radar speed measurement


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Critical Speed Equations

28

2 m

m

cR += Radius Equation

Critical Speed Yaw

Equation

Longitudinal Drag

Factor Equation

rfS 86.3=

d

SSf

fo

30

22

=


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C iti l S d Y D t


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Critical Speed Yaw Data

Observed Deceleration: 0.23g

ft1.51 ft 6"mo2

ft3030Chord2

ft1.281ft 3 3/8"mo1

ft3030Chord1

5.92 ftfps48.4

5'11"Track widthmph33Initial speed on radar

Summary of Critical Speed Yaw


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Calculations Corrected Radius 1: 84.29 feet

Corrected Radius 2: 71.29 feet Initial Speed 1; f = 0.77: 31.09 mph

Initial Speed 1; f = 0.83: 32.28 mph Final Speed 2; f = 0.77: 28.59 mph

Final Speed 2; f = 0.83: 29.69 mph Longitudinal Drag Factor: 0.18 calculated

Critical Speed Yaw Tests


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p

Minnesota Patrol Academy 2003 The Crown Vic was put into a critical speed yaw

at 38 mph as measured by Radar.

The VC-3000 was set in braking mode.

The x-axis (longitudinal) deceleration was0.181g at the beginning of the yaw.

A chord and middle ordinate was measuredwhen the rear tire began tracking outside the

corresponding front tire A second chord and middle ordinate was

measured from the end of the first chord

C iti l S d Y T t td


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A radius was calculated for each chord

If the vehicle is in a true critical speed yaw,there should be a reduction in speed from

the first radius to the second radius.

We will calculate the speeds using the

standard critical speed yaw equation and

the drag factor from the Taurus, which wasa non-ABS car.

Critical Speed Yaw Test contd


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The Taurus was put into a critical speed

yaw at 36 mph on the Radar. Its evidence was analyzed in the same

way as the evidence from the Crown Vic.



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28

2 m

m


Critical Speed Yaw

Equation

Longitudinal Drag

Factor Equation

rfS 86.3=

d

SSf

fo

30

22

=



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y p

Calculations Crown Vic Corrected Radius 1: 123.19 feet



X-axis deceleration measured: 0.181 Radar speed: 38 mph



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y p

Calculations Taurus Corrected Radius 1: 105.42 feet



X-axis deceleration measured: 0.192 Radar speed : 36 mph



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Montgomery, OH (July 2003) The Malibu was put into a critical speed yaw at 30 mph

as measured by Radar

The VC-3000 was set in continuous mode to measurethe lateral and longitudinal acceleration factors

The VC-3000 integrated speed was 29.5 mph.

The longitudinal deceleration factor was 0.26g right afterthe initial hard right steer.

A chord and middle ordinate was measured when therear tire began tracking outside the corresponding fronttire

A second chord and middle ordinate was measured fromthe end of the first chord

Critical Speed Yaw Test contd


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Critical Speed Yaw Test, cont d

A radius was calculated for each chord.

If the vehicle is in a true critical speed yaw, there

should be a reduction in speed from the firstradius to the second radius

We will calculate the speed using the standard

critical speed yaw equation and the drag slidingdrag factor from the Ford

The rear wheels of the Ford did not lock, so the

average used was 0.79, which is between theABS average of 0.82 and the sliding average of0.77.



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28

2 m

m


Critical Speed Yaw

Equation

Longitudinal Drag

Factor Equation

rfS 86.3=

d

SSf

fo

30

22

=

in65.50Track widthCritical Speed Yaw Analysis


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mph29.2Initial speed from Accelerometer:

mph30Initial speed on radar:

0.27Yaw Deceleration

mph24.33Critical Speedft2.167mo2

ft50.28Radius of CMin26mo2

ft53.01Radius of Tire markft30Chord2

mph28.91Critical Speedft1.542mo1

ft71.01Radius of CMin18.5mo1

ft73.74Radius of Tire markft30Chord1

* From Ford Crown Victoria test WITHOUT ABSft2.73Half Track*0.79Drag Factor

ft5.46Track width

Critical Speed Yaw of 2003 Chevy M alibu

(VC3000 Computer)


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-0.2

0

0.2

0.4

0.6

0.8

1

1.2

13 14 15 16 17 18 19

Time

G

's Longitudinal

Lateral

Post Yaw Braking

Initial value as calculated: 0.26

Critical Speed Yaw Tests


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Wyoming Academy October 2003 Tests were conducted during a TCR

Update course at the Wyoming LawEnforcement Academy.

The vehicle used was a 1989 Chevrolet

Caprice police package vehicle. Test skids were done with this vehicle on a

level portion of the test track.

The average for this vehicle withstandard brakes was 0.63.

Wyoming Tests contd


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Wyoming Tests, cont d

The vehicle was put into a critical speed yaw at46 mph as measured by Radar.

Two 30 foot chords were measured, with middleordinates of 0.52 ft and 0.57 ft respectively.

The two corrected radii were 213.6 ft. and 193.6ft, respectively.

The super-elevation at the middle ordinate

points was 0.01. The corrected lateral acceleration factor, f, was0.64.

Wyoming Tests contd


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Wyoming Tests, cont d.

The speed calculated from the first radii

was 45.13 mph. The speed calculated from the second

radius was 42.97 mph.

The calculated deceleration was 0.21g.

The accelerometer measured deceleration

was 0.21g.

Wyoming Tests contd


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Wyoming Tests, cont d.

A second critical speed test was conducted at a

Radar measured speed of 33 mph.

Using a similar analysis to the previous example,

the initial speed was calculated at 32.73 mph

and the second speed was 30.02 mph. The calculated deceleration was 0.18g.

The accelerometer measured deceleration was

0.20g.

What if its a Spin?


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What if it s a Spin?

The tire marks left in a post-impact spin

may sometimes look like a critical speedyaw.

They are not!

How may we deal the post-impact or other

rapid spin?

This vehicle has come to rest after


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This vehicle has come to rest after

impact, leaving the tire marks shown.If we confuse these tire marks with

critical speed yaw marks, we will

calculate an erroneous speed.

The speed we calculate will likely be

too high.

The following procedure will help us

determine a more accurate speed.

We will calculate drag factors for small

distance increments and will use the

combined speed equation.


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Plot the vehicle back at its

skid initiation point.

Draw a station line parallel to

the initial velocity vector of

the vehicle.

Draw offset lines

perpendicular to the station

line every 10 or 20 feet.

Plot the vehicle heading by


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g y

placing the vehicle back on

its tire marks, locating the

center of mass on the

appropriate offset line.

Determine velocity vector bearing

tangent to the ehicle path at each


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tangent to the vehicle path at each

CM location.The angle the vehicle makes with

respect to its velocity will be the

difference between bearing and

heading.

Use the CAD program to

determine the center of mass

distance moved between each

offset line.

Once we know this information, we

can calculate the drag factor for

this vehicle for each distance

increment.

We may then calculate speedusing a combined speed equation.

For this example, we will use

= 0.75

fndnf =Sin Distance


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Total

44.27

Total

96.1 ft

2.30.168.22419313.7

2.84.219.29216313.0

7.11.574.76613012.4

8.31.699.93311111.9

8.63.744.9928311.6

7.87.673.8986411.7

5.56.501.6694211.1

1.65.155.2071210.7

n nnsin+m

Post Impact Movement


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p

Use Combined Speed Equation:

S = 36.44 mph

Effective Drag Factor: 0.46Percentage of Braking: 0.61

)...(30 332211 nndfdfdfdfS ++++=

Sensitivity Analysis


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y y

The Critical Speed analysis depends upon

two variables: The Radius of the path of the Center of Mass

The lateral acceleration factor for the vehicle

How sensitive is the overall speed computation

to these two variables?

Effect of Radius


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The radius of the tire mark is calculatedfrom the chord and middle ordinatemeasurements.

Of these two, the radius equation is most

sensitive to the investigators ability tomeasure the middle ordinate.

We recommend the middle ordinate be

measured to the nearest 1/8 inch for a 30foot chord.

Effect of Radius, contd.


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Consider the following information:

The chord is 30 feet The actual middle ordinate measurement is 6

inches or 0.5 feet.

The middle ordinate is measured at 5 inches, or 0.458 feet.

The actual radius is 225.25 feet The radius from the measurement is 245.86 ft

The error is 20.61 feet, or +9.1%

Effect of Radius, contd.


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The speed calculated from the actual

radius is 50.17 mph with a nominal drag

factor of 0.75.

The speed calculated from the

measurement is 52.41 mph.

The difference is 2.24 mph, or 4.4%

Effect of Drag Factor


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We used a nominal 0.75 for the previouscalculations.

If we use a constant radius but vary thedrag factor, what is the effect?

For a radius of 225.25 feet and a dragfactor of 0.70, then S = 48.46 mph.

For a radius of 225.25 feet and a dragfactor of 0.80, then S = 51.81 mph.

The difference is 3.35 mph, or 6.6%.

Effect of Both Variables


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The radius varies between 225.25 feet and

245.86 feet.

The drag factor varies between 0.70 and 0.80

The speed calculated from the low values is

48.46 mph. The speed calculated from the high values is

54.13 mph.

The difference is 5.67 mph or 11.3% compared

to the nominal 50.17 mph.

Summary


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We have examined the Critical Speed Yaw analysis.

The technique has proved it usefulness over the years.

We measure the chord and middle ordinate for theoutside front tire immediately after the rear tire hascrossed over the front tire mark.

Use ABS Test skid data.

We must be sure the vehicle is actually in a criticalspeed yaw.

Examine the deceleration of the vehicle.

A nominal deceleration value for dry, hard roads is 0.20gfor the first third of the yaw.

Be very careful with both the drag factor determinationand the middle ordinate measurement!

With proper care, the method has been and remainsviable!

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Critical Speedy Aw